The power of factorization: resummation of super-leading logarithms & weak annihilation amplitudes
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Abstract
Factorization of physics associated with different scales is a powerful tool that enhances our understanding of high-energy processes. This thesis applies this concept within the framework of soft-collinear effective theory (SCET) to two different scenarios.
In the first part, a factorization theorem for non-global observables is derived, consisting of a hard function that captures physics at the high scale Q of the order of the partonic center-of-mass energy, convoluted with a low-energy matrix element that describes physics relevant at the soft veto scale Q0. On the example of gap-between-jet cross sections, the leading double-logarithmic corrections, known as super-leading logarithms, are resummed to all orders in perturbation theory by solving the renormalization-group equation of the hard function. It is shown that they give sizable contributions to partonic 2 → 2 scattering processes, but play a subdominant role for vector or Higgs boson production in association with one or no jet. In a second step, the analysis is extended to also include the imaginary parts of the large logarithms. We demonstrate that this “Glauber series”, which in the low-energy effective theory arises from Glauber-gluon exchanges between initial-state partons and collinear emissions from these partons, is parametrically suppressed with respect to the leading double-logarithmic corrections. Numerically, it suffices to consider up to four such exchanges to capture the relevant contribution to the cross section. For large Nc, we resum the Glauber series in closed form.
In the second part, we study weak annihilation contributions to exclusive non-leptonic B-meson decay amplitudes. By performing a systematic two-step matching of the relevant operators in the weak effective Hamiltonian on SCET-2, we identify several new partially endpoint-divergent contributions and so far unknown four- and five-particle distribution amplitudes of the B meson. We show how the endpoint divergences cancel between the standard QCD factorization contributions and some of these newly discovered ones. Therefore, this work establishes a subleading power factorization theorem for weak-annihilation amplitudes.